Generalization of equi-statistical convergence via weighted lacunary sequence with associated Korovkin and Voronovskaya type approximation theorems

Mohiuddine, S. A.; Alamri, Badriah A. S.

doi:10.1007/s13398-018-0591-z

Cited by 78 publications

(36 citation statements)

References 37 publications

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“…Moreover, the convergence methods are an active research area with important applications (see the recent monograph by Mursaleen [24]). For instance, there are applications in many fields, such as approximation theory [3,10,22,23,25,28]. On the other hand, from the point of view of infinite dimensional spaces, there are interesting results that characterize properties of normed spaces by means of some convergence types (see for instance [8,[16][17][18]).…”

Section: Introductionmentioning

confidence: 99%

On statistical convergence and strong Cesàro convergence by moduli

et al. 2019

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In this paper we will establish a result by Connor, Khan and Orhan (Analysis 8:47-63, 1988; Publ. Math. (Debr.) 76:77-88, 2010) in the framework of the statistical convergence and the strong Cesàro convergence defined by a modulus function f. Namely, for every modulus function f , we will prove that a f-strongly Cesàro convergent sequence is always f-statistically convergent and uniformly integrable. The converse of this result is not true even for bounded sequences. We will characterize analytically the modulus functions f for which the converse is true. We will prove that these modulus functions are those for which the statistically convergent sequences are f-statistically convergent, that is, we show that Connor-Khan-Orhan's result is sharp in this sense.

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Section: Introductionmentioning

confidence: 99%

On statistical convergence and strong Cesàro convergence by moduli

et al. 2019

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“…st A -lim x = L if, for every > 0, lim n k:|x k -L|≥ a nk = 0. In addition, A-statistical convergence results are studied in [13,22,23].…”

Section: A-statistical Convergencementioning

confidence: 99%

Approximation on a class of Szász–Mirakyan operators via second kind of beta operators

et al. 2020

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In the present article, we construct a new sequence of positive linear operators via Dunkl analogue of modified Szász-Durrmeyer operators. We study the moments and basic results. Further, we investigate the pointwise approximation and uniform approximation results in various functional spaces for these sequences of positive linear operators. Finally, we prove the global approximation and A-statistical convergence results for these operators.

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“…Nuray [29] and Mursaleen and Mohiuddine [25] defined this notion, respectively, for sequences of fuzzy numbers and in the setting of intuitionistic fuzzy normed space. Most recently, Mohiuddine and Alamri [20] defined the notion of weighted lacunary equistatistical convergence and, as an application, proved some approximation theorems.…”

Section: Introductionmentioning

confidence: 99%

Applications of Lacunary Sequences to Develop Fuzzy Sequence Spaces for Ideal Convergence and Orlicz Function

Raj

Mohiuddine

2020

Eur. J. Pure Appl. Math.

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In the present paper, we introduce and study ideal convergence of some fuzzy sequence spaces via lacunary sequence, infinite matrix and Orlicz function. We study some topological and algebraic properties of these spaces. We also make an effort to show that these spaces are normal as well as monotone. Further, it is very interesting to show that if $I$ is not maximal ideal then these spaces are not symmetric.

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Generalization of equi-statistical convergence via weighted lacunary sequence with associated Korovkin and Voronovskaya type approximation theorems

Cited by 78 publications

References 37 publications

On statistical convergence and strong Cesàro convergence by moduli

On statistical convergence and strong Cesàro convergence by moduli

Approximation on a class of Szász–Mirakyan operators via second kind of beta operators

Applications of Lacunary Sequences to Develop Fuzzy Sequence Spaces for Ideal Convergence and Orlicz Function

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